As a self hosted I only know Kanboard but it only do kanban afaik.

Otherwise I’m using " todoist " (obvious name). It’s a web app, with android app also. It provides several points of your list but not all:

• Several board/lists (called “project”).

• Can share any of the projects with someone else.

• Task + subtask with due date and priority (and even assign to someone).

• Keep history

• Add tags or comment to tasks and subtasks

• Several options for notifications

• Reminder/alaram, but only for paid version (never tried …)

I don’t think there are options for repeting tasks (maybe with the paid version). And no integration with home assistant provided.